Commentary on "Limitations of GCTA as a solution to the missing heritability problem" (abstract; pdf):

In a recent publication entitled "Limitations of GCTA as a solution to the missing heritability problem" Krishna Kumar et al. (2015 PNAS) claim that "GCTA applied to current SNP data cannot produce reliable or stable estimates of heritability". Here we show that those claims are false and that results presented by Krishna Kumar et al. are in fact entirely consistent with and can be predicted from the theory underlying GCTA.

The purported migrations that have formed the peoples of Britain have been the focus of generations of scholarly controversy. However, this has not benefited from direct analyses of ancient genomes. Here we report nine ancient genomes (~1 ×) of individuals from northern Britain: seven from a Roman era York cemetery, bookended by earlier Iron-Age and later Anglo-Saxon burials. Six of the Roman genomes show affinity with modern British Celtic populations, particularly Welsh, but significantly diverge from populations from Yorkshire and other eastern English samples. They also show similarity with the earlier Iron-Age genome, suggesting population continuity, but differ from the later Anglo-Saxon genome. This pattern concords with profound impact of migrations in the Anglo-Saxon period. Strikingly, one Roman skeleton shows a clear signal of exogenous origin, with affinities pointing towards the Middle East, confirming the cosmopolitan character of the Empire, even at its northernmost fringes.

To place our ancient genomes within a detailed British context, we next plotted these in a background PCA using 3,075 published genotypes from British3, Irish23 and southern Netherlands samples24. The modern samples were analysed using SNP genotypes at ~250,000 loci and projected into a single plot using smartpca (Fig. 3a). As in Burton et al.3 the first component of the variation was informative for the structure within Britain. Given the close ancestral relationships between these populations and their well-known history of migrational exchange, a substantial overlap between regional groups was both expected and observed. However, by considering median values, one can see a clear progression from Irish samples at one pole through Scottish, Welsh, English to the Dutch cohort at the other extreme. In this plot the York Romans cluster centrally close to the modern Welsh median value, along with the Iron-Age genome. The local Anglo-Saxon is placed differently, closest to modern East Anglians between the English and Dutch medians.

This first component also offers an opportunity to compare within the English sample. Figure 3b shows a boxplot of PC1 values for each subsample and structure is evident, with higher median values in Eastern regions such as East Anglia, East Midlands, intermediate values in the southern and western parts and lower values in the north and northwest. This pattern is more clearly seen in a geographical plot of interpolated values (Fig. 5a). When the York Romans are compared together with each modern cohort, they are most similar to the Welsh distribution of PC1 values and differ significantly from all other regional groups, apart from those from North and Northwest England (Mann–Whitney test; Fig. 3b, Supplementary Note 2 and Supplementary Table 13). An interesting difference is the marked one between the Driffield Terrace ancient and contemporary Yorkshire samples (P=0.003), implying regional discontinuity. It is also worth noting that the PC1 coordinate of the Anglo-Saxon individual is closer to the median PC1 value of East Anglians, possibly reflecting a more pronounced contribution of Germanic immigrants to eastern British populations. However, we note the inherent uncertainty in drawing inference from a single sample.